Introduction to Nanoscale Interface 5
orientational order parameter.
1,2
The former expresses the molecular
configuration describing the positional distribution of the heads of the
rod-molecules, and the latter expresses the orientational distribution of
the rod-like molecules. Interestingly, physico-chemical properties of the
molecular systems are dependent on these parameters. The electrical,
optical, and mechanical properties of the systems are described using
these parameters. Hence we have a chance to describe the specific
feature of organic material systems by using these parameters.
As the first step, we see how molecular system can be classified in
terms of orientational parameters. The orientational order parameter S
n
,
(n = 1, 2, 3) is defined using the thermodynamic average of the Legendre
polynomials, P
n
(cos θ) (n = 1, 2, and 3), of the orientational angle θ of
molecules.
1,2
In Fig. 1, the angle θ is defined as an angle from the
z-direction. Figure 1 shows a typical example of molecular systems.
Figure 1(a) shows the isotropic bulk materials, where rod molecules
are randomly distributed, thereby S
1
≡ <P
1
(cos θ)> = <cos θ> = 0, S
2
≡
<P
2
(cos θ)> = <(3 cos
2
θ − 1)/2> = 0, and S
3
≡ <P
3
(cos θ)> = <(5 cos
3
θ −
3 cos θ)/2> = 0. Figure 1(b) shows a case of nematic phase of bulk liquid
crystals, where the orientational direction of molecules is restricted and
molecules are totally distributed up and down directions, but there is no
distinction between up and down directions. Thereby, S
1
= 0, S
3
= 0, but
S
2
≠ 0. Figure 1(c) shows the monolayer composed of rod molecules,
where all molecules randomly orient upper direction. Thereby S
1
, S
2
,
S
3
≠ 0. From Fig. 1, it is found that the physical properties of nematic
liquid crystals can be described using S
2
. Actually we use this property,
S
2
≠ 0, in the application of liquid crystal displays. Similarly, the physical
properties of monolayers can be described using non-zero order
parameters S
1
, S
2
, and S
3
. Obviously, among these non-zero three
parameters, S
1
and S
3
are the specific parameters that are connected to
symmetry breaking. In other words, the specific physico-chemical
properties of monolayers can be expressed using non-zero S
1
and S
3
.
From the sketch of Fig. 1, we see that to generate spontaneous
polarization in molecular systems, alignment of rod molecules, i.e, S
1
≠ 0
is key. This means that preparation of sophisticated molecular system,
highly orientated at the nano-interface is needed, and development of
nanoscale interface fabrication method is truly expected.